- Title
- A necessary optimality condition for free knots linear splines: Special cases
- Creator
- Sukhorukova, Nadezda
- Date
- 2010
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/42146
- Identifier
- vital:3263
- Identifier
- ISSN:1348-9151
- Abstract
- In this paper, we study the problem of best Chebyshev approximation by linear splines. We construct linear splines as a max - min of linear functions. Then we apply nonsmooth optimisation techniques to analyse and solve the corresponding optimisation problems. This approach allows us to identify and introduce a new important property of linear spline knots (regular and irregular). Using this property, we derive a necessary optimality condition for the case of regular knots. This condition is stronger than those existing in the literature. We also present a numerical example which demonstrates the difference between the old and the new optimality conditions.
- Publisher
- Yokohama Publishers
- Relation
- Pacific Journal of Optimization Vol. 6, no. 2, Suppl. 1 (2010), p. 305-317
- Rights
- Copyright Yokohama Publishers
- Rights
- This metadata is freely available under a CCO license
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Nonsmooth optimization; Polynomial spline; Max - min functions
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